Sync isn't a backup system nor to be used as such. When you reconnected to Mozilla sync any sync data on sync server was replaced with the latest data from Firefox thus wiping clean any data that was there. What you should've done was do a proper Firefox browser Data backup of the profile, bookmarks, Login/pswd to a USB to restore them back to Firefox after reinstallation. But as this wasn't done any data there is now replaced with a clean Firefox data not with your data. As to your phone it will not work since the data will reset since the password no longer matches the account.

Sync isn't a backup system nor to be used as such. When you reconnected to Mozilla sync any sync data on sync server was replaced with the latest data from Firefox thus wiping clean any data that was there. What you should've done was do a proper Firefox browser Data backup of the profile, bookmarks, Login/pswd to a USB to restore them back to Firefox after reinstallation. But as this wasn't done any data there is now replaced with a clean Firefox data not with your data. As to your phone it will not work since the data will reset since the password no longer matches the account.

I have backup on external drive but it doesn't have few months of important data but more importantly I have ALL my data on my phone up to date. The question was about how to go about it correctly to sync the data from phone to PC profile and not wipe the phone as well.

Backup to drive will not work correctly as any data format will not correctly match the new Firefox install if you copy the data over could corrupt Firefox and cause more issues. The phone isn't the storage of the data so it will sync with the main device Desktop that has data stored on. You can't since the password has changed it will change since you changed the Desktop Firefox sync password already which means the Mozilla account sync will update to match the new settings. This is my interpretation of how the sync should work if all devices are properly connected to the sync server.